Table 309A. Distribution of Loss of Hearing Acuity
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316
T A B L E 310.ARCHITECTURAL
FIG.3.Attenuation
T A B L E 310A.OPTIMUM
ACOUSTICS (concluded)
coefficient nz per foot as a function of humidity.
R E V E R B E R A T I O N T I M E (FIGS. 4 A N D 5 )
T h e following figures give the recommendations of Knudsen and Harris for optimum
reverberation time for different types of rooms as a function of room volume. The optimum
times for speech rooms, motionpicture theaters, and school auditoriums are given by a
single line ; the optimum time for music by a broad band. Th e optimum reverberation time
is not the same for all kinds of music. F o r example, slow organ and choral music require
more reverberation than does a brilliant allegro composition played on woodwinds, piano,
or harpsicord.
The optimum reverberation time vs. frequency characteristic for a room can be obtained
from these charts in the following manner : After having specified the volume and purpose
of the room, determine the optimum reverberation time at 512 cycles from the upper chart.
Then, to obtain optimum reverberation time a t any other frequencies multiply the 512cycle
value by the appropriate ratio R which is given in the lower chart. Note that R is unity
for frequencies above 500 cycles, and is given by a band for frequencies below 500 cycles.
The ratio R for large rooms may have any value within the indicated band; preferred
ratios for small rooms are given by the lower part of the band.
(corztinued)
SMITHSONIAN PHYSICAL TABLES
T A B L E 310A.OPTIMUM
FIG.4.Optimum
REVERBERATION T I M E (FIGS. 4 A N D 5)
' < c o d I Ub&)
317
reverberation time as a function of volume of rooms for various types of
sound for a frequency of about 512 cycles per second.
1.6
1.6
1.4
4:
...
0 1.2
1.2
L
5
L
a! 1
1..c0I
0e
0I
00
100
FIG.S.Ratio
200
so0 400
600 8001000
2000 3000
5000
10.000
FREQUENCY IN cYcLea PER SECOND
of the reverberation time for various frequencies as a function of the
reverberation for 512 cycles per second.
SMITHSONIAN PHYSICAL TABLES
318
TABLES 311338.VISCOSITY
OF F L U I D S A N D S O L I D S *
The coefficient of viscosity of a substance is the tangential force required to
move a unit area of a plane surface with unit speed relative to another parallel
plane surface from which it is separated by a layer of the substance a unit thick.
Viscosity measures the temporary rigidity it gives to the substance.
Fluidity is the reciprocal of viscosity expressed in poises. Kinematic viscosity is absolute viscosity divided by density. Specific viscosity is viscosity
relative to that of some standard substance, generally water at some definite
temperature. The dimensions of viscosity are J4LlTl. It is generally expressed in cgs units as dynesecond per cm2 or poises.
The viscosity of fluids is generally measured by one of several methods
depending on the magnitude of the viscosity value to be measured. For vapors
and gases as well as for liquids of low viscosity, measurements of viscosity are
made by the rate of flow of the fluid through a capillary tube whose length is
great in comparison with its diameter. The equation generally used is
T],the
viscosity, 
 12852 (I+ A )
where y is the density (g/cm3), d and I are respectively the diameter and
length in cm of the tube, Q the volume in cm3 discharged in t sec, h the
Couette correction to the measured length of the tube, h the average head in cm,
m the coefficient of kinetic energy correction, mvu2/g,
necessary for the loss of
energy due to turbulent, in distinction from viscous, flow, g being the acceleration of gravity (cm/sec2), 2, the mean velocity in cm/sec. (See Herschel, Nat.
Eur. Standards Techn. Pap. Nos. 100 and 112, 19171918, for discussion
of this correction and h . )
For liquids of medium and high values of viscosity measurements are made
by Margule's method of observing the torque on the inner of two concentric
cylinders while the outer is rotated with constant angular speed with the viscous liquid filling the space between, or by noting the rate of fall of a solid
sphere through the liquid.
For the method of concentric cylinders the equation is
K8(R12R Z 2 ),
q, the viscosity, =
4&R,' R2, L
where K denotes the elastic constant of the torsion member supporting the
inner cylinder of radius R, cm and length L cm, .8is the angular displacement
of the inner cylinder from its position of equilibrium, R the angular speed of
the outer rotating cylinder of radius R , cm in the corresponding units employed to measure 8. The necessary corrections due to end effects of cylinders
of finite length are given in the reference.'O"
For the falling sphere method, the equation is that of Stokes law as modified
by R. G. Hunter: l o g
1 . R 2.2s )
T], the
('71,
2 R2(d,d2)
viscosity, = 9
(1+3.3:)
'
where y denotes the radius in cni of the crucible containing the liquid of density
d , (g/cni3), to a depth of Iz cni, R the radius in cm of the sphere of density d ,
(g/cm3), and Y the velocity (cni/sec) of the falling sphere.
* T h e data on viscosity were selected and arranged by George V. McCauley, Corning
Glkss Works.
Lillie, H . R., Journ. Amer. Cer. SOC.,
vol. 12, p. 505, 1929.
looHunter, R. G.. Journ. Amer. Cer. SOC.,
vol. 17, p. 123, 1934; Ann. d. Phys., ser. 4,
vol. 22, p. 287, 1907; vol. 23, p. 447, 1907.
SMITHSONIAN PHYSICAL TABLES
319
For very viscous materials, measurements of viscosity are made by noting
the rate of elongation of fibers under load or by observing the aperiodic inotioii
of an elastic system displaced from its position of equilibrium and damped by
the viscous material.
The formula for the rate of elongation of fibers as employed by H. R.
Lillie
is
Lxgxk
7, the viscosity, =
37rR2E '
where R is the radius in cni of the fiber of effective length, L (cm), g the
mass in grams of the attached load, k the acceleration of gravity (cm/sec2),
and E the rate of elongation in cm/sec.
For the aperiodic motion of the system consisting of the suspended inner
cylinder of Margule's apparatus described above, the formula is
K(t,t,) log e R Z 2  R l 2
7 , the viscosity, =
el R12RZZ
4XL log,, 
)'
(
0,
where t2 and t , denote the times in seconds of angular positions O2 and 8, of the
suspended system from its position of equilibrium. The other characters have
the same significance as in the formula above for the rotating cylinder method
of measuring viscosity. (For reference, see footnote 105.)
The viscosity of solids may be measured in relative terms by the damping
of the oscillations of suspended wires (see Table 323). Ladenburg (1906)
gives the viscosity of Venice turpentine at 15.3" as 1300 poises; Trouton and
Andrews (1904) of pitch at O o , 51 x lo'", at 15") 1.3 x 1O'O; of shoemaker's
~ of soda glass at 575", 11 x lo'*; Deeley (1908) of glacier
wax at 8", 4 . 7 lo6;
ice as 12 x 1013.
"'Lillie, H. R., Journ. Amer. Cer. SOC.,vol. 14, p. 502, 1931.
T A B L E 311.VISCOSITY
OF W A T E R I N C E N T I P O I S E S
(Temperature variation)
Part 1.Low
Vi?
CP
"C
Viscos1ty
cp
"C
20
21
22
23
24
1.0050
.9810
.9579
.9358
.9142
30
31
32
33
34
,8007
.7840
.7679
.7523
.7371
25
26
27
28
29
.8337
3737
,8545
.8360
.8180
35
36
37
38
39
,7225
.7085
.6947
.6814
.6685
"C
cos1ty
CP
"C
Viscosity
cp
"C
0
1
2
3
4
1.7921
1.7313
1.6728
1.6191
1.5674
10
11
12
13
14
1.3077
1.2713
1.2363
1.2028
1.1709
5 1.5188
15
16
17
18
19
1.1404
1.1111
1.0828
1.0559
1,0299
6
7
8
9
1.4728
1.4284
1.3860
1.3462
Viy
cosrty
temperature
(continued)
SMITHSONIAN PHYSICAL TABLES
Viy
cos1ty
cp
"C
Viscosity
cp
,5494
,5404
S315
,5229
S146
60
65
70
75
80
.4688
.4355
.4061
.3799
.3565
Vis.
cos1ty
cp
"C
40
41
42
43
44
.6560
.6439
,6321
.6207
.6097
50
51
52
53
54
45
46
47
48
49
S988
.5883
55 .SO64
56 .4985
57 .4907
58 .4832
59 .4759
.5782
.5683
S588
85 .3355
90 3165
95 .2994
100 2838
153 .181
320
O F W A T E R I N CEN TIPOIB ES (concluded)
T A B L E 311.VISCOSITY
Pa rt 2.High
viscosity
cp
"C
130
135
140
145
150
"'Based
...
...
...
.I99
.191
temperature"'
"C
viscosity
cp
"C
cp
"C
155
160
165
170
175
.184
.178
.173
.I66
.I60
180
185
190
195
200
.I55
205
210
215
220
225
Vi,s
Vis
COSItY
COSltY
.I51
.146
.I43
.139
cp
.136
.134
.131
.129
.128
on measurements by Shugayev, V., Journ. Exp. and Theoret. Phys. ( U . S . S . R . ) , vol. 4,
p. 760, 1934.
P a rt 3.Viscosity
o f heavy water in centipoises
9.65% DzO; dn" = 1.10495
"c
4
5
6
7
112
Via
Viy
cos1ty
CD
"c
COS'tY
CD
2.25
2.10
1.99
1.90
8
9
10
11
1.81
1.73
1.67
1.61
"C
Viy
cos1ty
cp
"c
12
13
14
15
1.56
1.51
1.46
1.41
16
17
18
19
VisCOSltY
CD
1.37
1.33
1.29
1.25
Data by Lemond, Henri. Cornpt. Rend., vol. 212, p. 81, 1941.
T A B L E 312.VISCOSITY
O F AL COHOL W AT E R
M I X T U R E S I N CENTlPOlSES
(Temperature variation)
Percentage by weight of ethyl alcohol
"C
0
5
10
is
20


0
10
20
30
35
40
45
50
60
70
80
90
100
1.792
1.519
1.308
1.140
1.005
3.311
2.577
2.179
1.792
1.538
5.319
4.065
3.165
2.618
2.183
6.94
5.29
4.05
3.26
2.71
7.25
5.62
4.39
3.52
2.88
7.14
5.59
4.39
3.53
2.91
6.94
5.50
4.35
3.51
2.88
6.58
5.26
4.18
3.44
2.87
5.75
4.63
3.77
3.14
2.67
4.762
3.906
3.268
2.770
2.370
3.690
3.125
2.710
2.309
2.008
2.732
2.309
2.101
1.802
1.610
1.773
1.623
1.466
1.332
1.200
2.35
2.00
1.71
1.473
1.284
1.124
2.35
2.02
1.72
1.482
1.289
1.132
2.39
2.02
1.73
1.495
1.307
1.148
2.40
2.02
1.72
1.499
1.294
1.155
2.23
1.93
1.66
1.447
1.271
1.127
2.037
1.767
1.529
1.344
1.189
1.062
1.748
1.531
1.355
1.203
1.081
968
1.424 1.096
1.279 1.003
1.147 .914
1.035 ,834
.939 .764
348 .702
.a5
.893
.727
.601
.907
.740
.609
,913
.740
.612
,902
.729
.604
.856
.695

.789
.650

25
30
35
40
45
50
394 1.323 1.815 2.18
301 1.160 1.553 1.87
.722 1.006 1.332 1.58
.656 .907 1.160 1.368
.599 312 1.015 1.189
.549 ,734 907 1.050
60
70
80
.469
.406
.356
.609
.514
.430
.736
.608
SO5
SMITHSONIAN PHYSICAL TABLES
,834
.683
.567
,725
.598
,704
.589
.592
504
 